53,294 research outputs found
Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian
Based on the technique of integration within an ordered product (IWOP) of
operators we introduce the Fresnel operator for converting Caldirola-Kanai
Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel
operator with the parameters A,B,C,D corresponds to classical optical Fresnel
transformation, these parameters are the solution to a set of partial
differential equations set up in the above mentioned converting process. In
this way the exact wavefunction solution of the Schr\"odinger equation governed
by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed
number state. The corresponding Wigner function is derived by virtue of the
Weyl ordered form of the Wigner operator and the order-invariance of Weyl
ordered operators under similar transformations. The method used here can be
suitable for solving Schr\"odinger equation of other time-dependent
oscillators.Comment: 6 pages, 2 figure
The Radio and Gamma-Ray Luminosities of Blazars
Based on the -ray data of blazars in the third EGRET catalog and
radio data at 5 GHz, we studied the correlation between the radio and
-ray luminosities using two statistical methods. The first method was
the partial correlation analysis method, which indicates that there exist
correlations between the radio and -ray luminosities in both high and
low states as well as in the average case.
The second method involved a comparison of expected -ray luminosity
distribution with the observed data using the Kolmogorov--
Smirnov (KS) test. In the second method, we assumed that there is a
correlation between the radio and -ray luminosities and that the
-ray luminosity function is proportional to the radio luminosity
function. The KS test indicates that the expected gamma-ray luminosity
distributions are consistent with the observed data in a reasonable parameter
range. Finally, we used different -ray luminosity functions to estimate
the possible 'observed'
-ray luminosity distributions by GLAST.Comment: 8 pages, 4 figures, one table, PASJ, 53 (2001
Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process
We present an adaptive method for the automatic scaling of Random-Walk
Metropolis-Hastings algorithms, which quickly and robustly identifies the
scaling factor that yields a specified overall sampler acceptance probability.
Our method relies on the use of the Robbins-Monro search process, whose
performance is determined by an unknown steplength constant. We give a very
simple estimator of this constant for proposal distributions that are
univariate or multivariate normal, together with a sampling algorithm for
automating the method. The effectiveness of the algorithm is demonstrated with
both simulated and real data examples. This approach could be implemented as a
useful component in more complex adaptive Markov chain Monte Carlo algorithms,
or as part of automated software packages
Polarization and Variations of BL Lacertae Objects
BL Lacertae objects are an extreme subclass of AGNs showing rapid and
large-amplitude variability, high and variable polarization, and core-dominated
radio emissions. If a strong beaming effect is the cause of the extreme
observation properties, one would expect that these properties would be
correlated with each other. Based on the relativistic beaming model,
relationships between the polarization and the magnitude variation in
brightness, as well as the core- dominance parameter are derived and used
statistically to compare with the observational data of a BL Lacertae object
sample. The statistical results are consistent with these correlations, which
suggests that the polarization, the variation, and the core-dominance parameter
are possible indications of the beaming effect.Comment: 6 pages, two figures, one table, some revisions. PASJ, 53 (2001
Basic properties of Gamma-ray loud blazars
In this paper, a method is proposed to determine the basic properties of
-ray loud blazars, among them the central black hole mass, M, the
Doppler factor, , the propagation angle of the -rays with
respect to the symmetric axis of a two-temperature accretion disk, , and
the distance (i.e. the height above the accretion disk), d at which the
-rays are created, for seven -ray loud blazars with available
GeV variability timescales and in which the absorption effect of a -ray
and the beaming effect have been taken into account. Our results indicate that,
if we take the intrinsic -ray luminosity to be times the
Eddington luminosity, , the masses of the
blazars are in the range of , the Doppler
factors () lie in the range of 0.57 to 5.33 the angle () is in
the range of to 43 and the distance (d) is in the range
of 26R_{g} to 411R_{g}. Our model results are independent of -ray
emission mechanisms but they do depend on the X-ray emission mechanism of the
accretion disk.Comment: 14 pages, 3 tables, A&A accepte
Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation
In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex
continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother
wavelets family. In this work we present the inversion formula and Parsval
theorem for CCWT by virtue of the entangled state representation, which makes
the CCWT theory complete. A new orthogonal property of mother wavelet in
parameter space is revealed.Comment: 4 pages no figur
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